GIF format seems to be the best use for general web design. GIF is easy to work with, easy to load. In a time where compatible is very important, this is a great format to go with. It has given me little trouble, except with power point. In several Power Point Presentations, I had all my GIF photos turn black. I have been using most.
PNG format has been a great replacement for the other formats. One of the most important reasons for PNG is that it provides a patent-free replacement for GIF. It has been very simple to use and very compatible. I use it most with my Power Point Presentations and a lot of my web design.
JPEG is the format that I do use the most, mainly because it seems that most of the files I get are in JPEG. JPEG is also the format that Photo Shop uses when you select the “save for web option” as a default. It has a lot of great compression option, but I really don’t under most of them.